Hi,

I think Allard that Deewakar probably meant Hydrodynamic stability in the sense Hydrodynamics stability theory not just hydrodynamically stable flows.

Hydrodynamic stability theory is a framework within fluid dynamics strongly related to dynamical system theory from a mathematical point of view (since it makes use of notions such as fixed points, stable and unstable directions, so on so forth ...). As you have mentioned, it allows you to get a better understanding of:

• When does the flow changes from steady to unsteady, i.e. at what Reynolds number? (Keep in mind that transition to unsteadiness does not always mean transition to turbulence).
• How does it become unstable? What does the perturbation looks like? What is the underlying instability mechanisms?
• ...

The knowledge gained by stability theory, though it often relies on a linear hypothesis which is not always true, allows you to have a better understanding of the physics of flow. If you are then interested in controlling this flow, be it keeping it laminar at higher Reynolds number (e.g. aerodynamics applications) or trying to promote turbulence at lower Reynolds number (e.g. chemical reactors), you can then design your control in a more efficient way since you know when, where and how the flow might transition.

Feel free to check on the materials I have posted on my profile. They all deal with different aspect of Hydrodynamics linear stability and various flow configurations. Hope this will be helpful.

Hydrodynamic stability basically just means that there are no instabilities in a system. That doesn't necessarily mean that nothing moves. For example, a smooth constant flow through a tube is hydrodynamically stable. On the other hand, if you have two fluid layers with the denser fluid on top, that is an unstable system, because the denser fluid will tend to move downward (Rayleigh-Taylor instability). Once all the dense fluid has moved to the bottom, the system has become hydrodynamicaly stable.

I'm not entirely sure what you mean with 'technological significance'. Instabilities cost energy (for example, turbulence over the wing of a plane or behind a car increases drag). In that sense you want to avoid them and create a system that is as stable as you can make it.

I'm not sure if this helps you. Can you give me an indication of the kind of situation that you're interested in?

Hi,

I think Allard that Deewakar probably meant Hydrodynamic stability in the sense Hydrodynamics stability theory not just hydrodynamically stable flows.

Hydrodynamic stability theory is a framework within fluid dynamics strongly related to dynamical system theory from a mathematical point of view (since it makes use of notions such as fixed points, stable and unstable directions, so on so forth ...). As you have mentioned, it allows you to get a better understanding of:

• When does the flow changes from steady to unsteady, i.e. at what Reynolds number? (Keep in mind that transition to unsteadiness does not always mean transition to turbulence).
• How does it become unstable? What does the perturbation looks like? What is the underlying instability mechanisms?
• ...

The knowledge gained by stability theory, though it often relies on a linear hypothesis which is not always true, allows you to have a better understanding of the physics of flow. If you are then interested in controlling this flow, be it keeping it laminar at higher Reynolds number (e.g. aerodynamics applications) or trying to promote turbulence at lower Reynolds number (e.g. chemical reactors), you can then design your control in a more efficient way since you know when, where and how the flow might transition.

Feel free to check on the materials I have posted on my profile. They all deal with different aspect of Hydrodynamics linear stability and various flow configurations. Hope this will be helpful.

Jean-Christophe, Thanks, now the question makes more sense to me. Not sure if there is a way to explain this quickly, though. This is really a huge field.

Hi,

As I understood, Deewakar was asking about a technological importance of  hydrodynamic stability theory, As it was already mentioned here, this field is huge. One of the real life application, or usage of this theory is in a drag reduction and turbulence control... Actually, delay and/or control of transition to turbulence...

For example, if you manage to make such a pipe wall, or plane wing surface,  that allow you to reduce a drag by controlling a transition to turbulence, then your win would be billions and billions... :)

Dear all,

thank you for your kind reply. I am mainly looking for application in near critical fluids. I read some where regarding its application in space technology in cryogenic conditions but couldn't dig much. 

If some may  throw light on this as aspect and applications in bio-medical

Thanks

Hi again,

For bio-medical related applications, you can check the papers by Spencer Sherwin (Imperial College, UK) and Hugh Blackburn (Monash University, Australia). They have investigated the linear stability of the flow in a stenotic pipe (rather crude model of stenotic artery to be fairly honest but it is almost the best we can do today regarding the stability of three-dimensional flows) with both steady and pulsatile inflow boundary conditions.

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Hi all

I need some suggestion reg basic text to study this topic. I started with Hydrodynamic Stability by Drazin and Reid. However, it seems to assume alot from the reader.

Isn't there any simple text for a beginner. Also any pre-requisites one may need.

Thanks

Hi,

Well, Drazin & Reid is a fairly good book for beginners. Then, it kind of depends on your background in mathematics and fluid dynamics obviously. Another great book for beginner I believe is: Hydrodynamic instabilities, by François Charru. This is actually the one I first bought when I started to study linear instabilities in fluid dynamics.

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Hi,

I have started with Introduction to Hydrodynamic Stability by Drazin. May I know what mathematical pre-requisites are required

Hi all,

Kindly correct me if I am wrong in getting an overview of the subject so far. What we are trying to study is that there is a flow or fluid at rest under certain conditions  ( for example flow in a pipe etc.) Now say some disturbance is introduced, this may be external or due to change in some flow parameter , say Re number, which effects the flow due to some reason (may be additional energy that is added etc. In the realm of such disturbance we are basically trying to analyze how the flow will behave subjected to such conditions, how to restore back the original if required and so on.

Deewakar 

Deewakar, como estava fora de ResearchGATE algum tempo não vi sua pergunta ou sugestões que lhe deu, mas para quem é um novato como você, eu sugiro que você leia algo mais físico e menos matemático para entender o que você está estudando.

Antes de ler a Drazin Gostaria de sugerir o livro TRITTON, JD 1988, "Dinâmica de Fluidos físicos", muito mais compreensível do que o Drazin.

I recently started reading the book from Francois Charru. Very nice and complete book with excellent exercises at the end of each chapter. However, I could not find any kind of solution manual, which makes the book hard for self study. Does any of you have the solutions?